Question

The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

Answer 1

Let the interior angles of the pentagon be $4x,5x,6x,7x,5x$.

Their sum $=4x+5x+6x+7x+5x=27x$

Sum of interior angles of a polygon $=(n-2)\times {180}^o=(5-2)\times {180}^o={540}^o\therefore 27x=540\Rightarrow x=\frac{540}{27}\Rightarrow x={20}^o\therefore Anglesare4\times {20}^o={80}^{o}5\times {20}^o={100}^{o}6\times {20}^o={120}^{o}7\times {20}^o={140}^{o}5\times {20}^o={100}^o$